Automated Market Makers

Quantum and Classical Machine Learning in Decentralized Finance: Comparative Evidence from Multi-Asset Backtesting of Automated Market Makers ArXiv ID: 2510.15903 “View on arXiv” Authors: Chi-Sheng Chen, Aidan Hung-Wen Tsai Abstract This study presents a comprehensive empirical comparison between quantum machine learning (QML) and classical machine learning (CML) approaches in Automated Market Makers (AMM) and Decentralized Finance (DeFi) trading strategies through extensive backtesting on 10 models across multiple cryptocurrency assets. Our analysis encompasses classical ML models (Random Forest, Gradient Boosting, Logistic Regression), pure quantum models (VQE Classifier, QNN, QSVM), hybrid quantum-classical models (QASA Hybrid, QASA Sequence, QuantumRWKV), and transformer models. The results demonstrate that hybrid quantum models achieve superior overall performance with 11.2% average return and 1.42 average Sharpe ratio, while classical ML models show 9.8% average return and 1.47 average Sharpe ratio. The QASA Sequence hybrid model achieves the highest individual return of 13.99% with the best Sharpe ratio of 1.76, demonstrating the potential of quantum-classical hybrid approaches in AMM and DeFi trading strategies. ...

Optimal Fees for Liquidity Provision in Automated Market Makers ArXiv ID: 2508.08152 “View on arXiv” Authors: Steven Campbell, Philippe Bergault, Jason Milionis, Marcel Nutz Abstract Passive liquidity providers (LPs) in automated market makers (AMMs) face losses due to adverse selection (LVR), which static trading fees often fail to offset in practice. We study the key determinants of LP profitability in a dynamic reduced-form model where an AMM operates in parallel with a centralized exchange (CEX), traders route their orders optimally to the venue offering the better price, and arbitrageurs exploit price discrepancies. Using large-scale simulations and real market data, we analyze how LP profits vary with market conditions such as volatility and trading volume, and characterize the optimal AMM fee as a function of these conditions. We highlight the mechanisms driving these relationships through extensive comparative statics, and confirm the model’s relevance through market data calibration. A key trade-off emerges: fees must be low enough to attract volume, yet high enough to earn sufficient revenues and mitigate arbitrage losses. We find that under normal market conditions, the optimal AMM fee is competitive with the trading cost on the CEX and remarkably stable, whereas in periods of very high volatility, a high fee protects passive LPs from severe losses. These findings suggest that a threshold-type dynamic fee schedule is both robust enough to market conditions and improves LP outcomes. ...

Impermanent loss and Loss-vs-Rebalancing II ArXiv ID: 2502.04097 “View on arXiv” Authors: Unknown Abstract This paper examines the relationship between impermanent loss (IL) and loss-versus-rebalancing (LVR) in automated market makers (AMMs). Our main focus is on statistical properties, the impact of fees, the role of block times, and, related to the latter, the continuous time limit. We find there are three relevant regimes: (i) very short times where LVR and IL are identical; (ii) intermediate time where LVR and IL show distinct distribution functions but are connected via the central limit theorem exhibiting the same expectation value; (iii) long time behavior where both the distribution functions and averages are distinct. Subsequently, we study how fees change this dynamics with a special focus on competing time scales like block times and ‘arbitrage times’. ...

Impermanent loss and loss-vs-rebalancing I: some statistical properties ArXiv ID: 2410.00854 “View on arXiv” Authors: Unknown Abstract There are two predominant metrics to assess the performance of automated market makers and their profitability for liquidity providers: ‘impermanent loss’ (IL) and ’loss-versus-rebalance’ (LVR). In this short paper we shed light on the statistical aspects of both concepts and show that they are more similar than conventionally appreciated. Our analysis uses the properties of a random walk and some analytical properties of the statistical integral combined with the mechanics of a constant function market maker (CFMM). We consider non-toxic or rather unspecific trading in this paper. Our main finding can be summarized in one sentence: For Brownian motion with a given volatility, IL and LVR have identical expectation values but vastly differing distribution functions. ...

A Tick-by-Tick Solution for Concentrated Liquidity Provisioning ArXiv ID: 2405.18728 “View on arXiv” Authors: Unknown Abstract Automated market makers with concentrated liquidity capabilities are programmable at the tick level. The maximization of earned fees, plus depreciated reserves, is a convex optimization problem whose vector solution gives the best provision of liquidity at each tick under a given set of parameter estimates for swap volume and price volatility. Surprisingly, early results show that concentrating liquidity around the current price is usually not the best strategy. ...

Improving Capital Efficiency and Impermanent Loss: Multi-Token Proactive Market Maker ArXiv ID: 2309.00632 “View on arXiv” Authors: Unknown Abstract Current approaches to the cryptocurrency automated market makers result in poor impermanent loss and capital efficiency. We analyze the mechanics underlying DODO Exchange’s proactive market maker (PMM) to probe for solutions to these issues, leading to our key insight of multi-token trading pools. We explore this paradigm primarily through the construction of a generalization of PMM, the multi-token token proactive market maker (MPMM). We show via simulations that MPMM has better impermanent loss and capital efficiency than comparable market makers under a variety of market scenarios. We also test multi-token generalizations of other common 2-token pool market makers. Overall, this work demonstrates several advantages of multi-token pools and introduces a novel multi-token pool market maker. ...